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This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices. In addition, this unique work examines the essentials of abstract semigroup theory and its application to concrete semigroups of matrices. This substantially revised text includes exercises at various levels at the end of each section and includes the best available proofs on the most important theorems used in a book, making it suitable for a one semester course on semigroups. In addition, it could also be used as a main text or supplementary material for courses focusing on probability on algebraic structures or weak convergence.
This book is ideally suited to graduate students in mathematics, and students in other fields, such as engineering and the sciences with an interest in probability. Students in statistics using advanced probability will also find this book useful.
This book is ideally suited to graduate students in mathematics, and students in other fields, such as engineering and the sciences with an interest in probability. Students in statistics using advanced probability will also find this book useful.
From the reviews of the second edition:
`A well-written book...This is elegant mathematics, motivated by examples and presented in an accessible way that engages the reader.'
International Statistics Institute, December 1996
`This beautiful book...guides the reader through the most important developments...a valuable addition to the library of the probabilist, and a must for anybody interested in probability on algebraic structures.'
Zentralblatt für Mathematik und ihre Grenzgebiete-Mathematical Abstracts
`This well-written volume, by two of the most successful workers in the field....deserves to become the standard introduction for beginning researchers in this field.'
Journal Royal Statistical Society
"Högnäs and Mukherjea have made substantial contributions to the subject themselves and present their work and that of others in a unified way. ... For students ... this book is an excellent account of the long-term behavior of random transformations. It organizes the ideas very well and its development of the theory is clear and rigorous. ... a useful reference for anyone interested in random walks on semigroups and groups. ... will be valuable to any reader who wishes to learn the subject ... ." (George Willis, SIAM Review, Vol. 54 (2), 2012)
`A well-written book...This is elegant mathematics, motivated by examples and presented in an accessible way that engages the reader.'
International Statistics Institute, December 1996
`This beautiful book...guides the reader through the most important developments...a valuable addition to the library of the probabilist, and a must for anybody interested in probability on algebraic structures.'
Zentralblatt für Mathematik und ihre Grenzgebiete-Mathematical Abstracts
`This well-written volume, by two of the most successful workers in the field....deserves to become the standard introduction for beginning researchers in this field.'
Journal Royal Statistical Society
"Högnäs and Mukherjea have made substantial contributions to the subject themselves and present their work and that of others in a unified way. ... For students ... this book is an excellent account of the long-term behavior of random transformations. It organizes the ideas very well and its development of the theory is clear and rigorous. ... a useful reference for anyone interested in random walks on semigroups and groups. ... will be valuable to any reader who wishes to learn the subject ... ." (George Willis, SIAM Review, Vol. 54 (2), 2012)